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Quasitriangular and Differential Structures on Bicrossproduct Hopf Algebras

✍ Scribed by Edwin Beggs; Shahn Majid

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 292 KB
Volume: 219
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7845

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✦ Synopsis

Let X s GM be a finite group factorisation. It is shown that the quantum Ž .

Ž . double D H of the associated bicrossproduct Hopf algebra

This provides a class of bicrossproduct Hopf algebras which are quasitriangular. We also construct a subgroup Y X associated to every order-reversing automor-Ž . phism of X. The corresponding Hopf algebra kX d . k Y has the same coalgebra as H. Using related results, we classify the first order bicovariant differential calculi on H in terms of orbits in a certain quotient space of X.

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